They said that the Archbishop, Dr Rowan Williams, would fail to avert a schism because liberals were determined to press ahead with their pro-gay agenda.

Instead, they called on Dr Williams to acknowledge that there were now two distinct Churches and negotiate an “orderly separation” to preserve a traditional identity for Anglicanism.

Liberals warned that such an action could lead to civil war in the Church.

The comments from the bishops of Winchester and Exeter, came as bishops at the Lambeth Conference released their final briefing paper on plans to solve the crisis over homosexuality.

Among the key proposals, they suggest a new framework that could censure rebellious Churches and a central “pastoral forum” to settle disputes.

However, the Rt Rev Michael Scott-Joynt, the Bishop of Winchester, said that the Archbishop’s plan to maintain unity lacked a sense of urgency and was unlikely to work.

“The Lambeth Conference is required to do something rather than live down to the worst expectations of the bishops who stayed away,” he said.

“We need to negotiate a separation in the Communion sooner rather than later, to leave the strongest possibility of remaining in some kind of fellowship.”

Bishop Scott-Joynt said that he was concerned that traditional Churches in Africa would break away unless the Lambeth Conference delivers a clear definition of what Anglicanism represents in the final report.

About 250 bishops have boycotted the conference and undermined the authority of the Archbishop of Canterbury by setting up a movement that could appeal to bishops disillusioned with an unsatisfactory outcome to the summit

“The most unhealthy thing would be to allow the debate to continue for a long time,” said Bishop Scott-Joynt. “We would have only ourselves to blame if more of the provinces go their own way.”

His fears were echoed by the Rt Rev Michael Langrish, the Bishop of Exeter, who accused America’s Episcopal Church, which consecrated Anglicanism’s first openly gay bishop, of being selfish and establishing a rival Church.

He said: “The vast majority want to take steps towards restoring Communion, but a smaller group base the language of Communion on feelings — what it means to me, what can I get from it.”

Bishop Langrish said that there was an “inexorable logic” that there should be one core Communion with the more liberal Churches pushed to the margins.

He added: “A major question is how we move towards that point — the highest degree of fellowship whilst allowing for an orderly separation.”

However, such a split would not only affect the Anglican Communion, but would threaten the unity of the Church of England, which is also bitterly divided.

The Rev Giles Goddard, the chairman of Inclusive Church, a liberal lobbying group, accused the bishops of trying to derail the report.

“The traditionalists are in the minority and an increasing number in the Church of England would side with the American Church now,” he said. “The people in the pew wonder what all the fuss is about.”

Bishop Scott-Joynt cast doubt on plans for an Anglican Covenant, or rule book of beliefs, which Dr Williams hopes will bind the Communion together behind a shared set of tenets.

“My greatest worry about the covenant is who’ll still be around to use it,” he said.

The final report from the bishops said that the Covenant would be “costly and self-limiting”, but that there is an “overall willingness” for it to happen.

They added that “there have been positive effects in parts of Canada, the US and England when homosexual people are accepted as God’s children, and are treated with dignity”.